A067920 Engel expansion of sin(2).

2, 2, 2, 4, 11, 14, 57, 100, 1778, 2355, 7690, 21334, 89831, 126718, 365351, 665175, 914152, 1469797, 3554254, 25042522, 190651419, 580715831, 1803513148, 3705699670, 44927205487, 232354919706, 1600668490436, 7538452976365, 12294187702836, 28817421277388

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Mathematica

EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[Sin[2], 7!], 30] (* Georg Fischer, Nov 20 2020 *)

Prog

(PARI): r=sin(2); for(i=1, 20, s=r*ceil(1/r)-1; print1(ceil(1/r), ", "); r=s); /* Benoit Cloitre [amended by Georg Fischer, Nov 20 2020] */

Crossrefs

See A006784 for explanation of Engel expansions.

Sequence in context: A130707 A131562 A260786 * A107902 A142974 A259856

Adjacent sequences: A067917 A067918 A067919 * A067921 A067922 A067923

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 03 2002

Extensions

a(1)=2 inserted and a(29),a(30) from Georg Fischer, Nov 20 2020

Status

approved